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I need help solving the problem number 8 of the image attached in this post.

The answer is NO = 30 & OP = 10 (root)34

Please help with the step by step process and tips and tricks for the solution.

Thanks,Pashmi

Welcome to GMAT Club. Below is a solution to your question.

What are the lengths of sides NO and OP in triangle NOP below?

Notice that triangles NOP and the smaller triangle within it (with the lengths of sides 24 and 40) are similar: they share the same angle P and both are right angled, so all their three angles are equal.

In similar triangles the ratio of the corresponding sides are equal (corresponding sides are the sides opposite the same angles). So, \frac{NO}{24}=\frac{NP}{40} --> \frac{NO}{24}=\frac{40+10}{40} --> NO=30.

Next, since NO=30 then OP=\sqrt{NO^2+NP^2}=\sqrt{30^2+50^2}=10\sqrt{34}.

Re: What are the lengths of sides NO and OP in triangle NOP [#permalink]
14 Nov 2013, 17:15

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